Joule-Thomson Coefficient Calculator

The Joule-Thomson effect is the temperature change a real gas experiences when it expands through a valve or porous plug at constant enthalpy (no heat exchanged, no external work done). Real gases can either cool or warm during this process, depending on their temperature relative to their inversion temperature.

μ_JT = (2a/(RT) − b)/Cp, a Van der Waals-based approximation, where a and b are the Van der Waals constants, T is temperature, R is the gas constant, and Cp is molar heat capacity at constant pressure.

An ideal gas has no intermolecular forces (a=0) and no molecular volume correction relevant to this effect, so there is no internal energy change associated with changing the average distance between molecules during expansion, meaning no temperature change occurs, this effect exists specifically because of real-gas non-ideality.

Inversion temperature is the temperature at which the Joule-Thomson coefficient equals zero, below it the gas cools on expansion (μ_JT positive), above it the gas warms instead (μ_JT negative). This calculator computes it as Tinv=2a/(Rb) from the Van der Waals constants.

Helium and hydrogen have very low inversion temperatures (helium's real inversion temperature is around 40 K, hydrogen's around 200 K), well below room temperature, so at room temperature they actually warm on Joule-Thomson expansion. They must first be pre-cooled below their inversion temperature before expansion cooling can work to liquefy them.

It is the basis for many industrial gas liquefaction processes (like producing liquid nitrogen or liquid natural gas), as well as household refrigeration and air conditioning, where the working fluid cools significantly as it expands through an expansion valve.

The exact Joule-Thomson coefficient requires either experimentally measured data or a more sophisticated equation of state than the two-parameter Van der Waals model. This calculator's simplified Van der Waals-based formula gives a reasonable order-of-magnitude estimate and captures the correct qualitative behavior (sign, rough inversion temperature) but will differ somewhat from precisely measured values.

No, only gases whose inversion temperature is above room temperature (like CO2, N2, and O2) reliably cool on Joule-Thomson expansion at everyday temperatures. Gases with very low inversion temperatures (like helium and hydrogen) actually warm slightly on expansion at room temperature.

It is measured by forcing a gas through a porous plug or throttling valve under carefully controlled adiabatic (no heat loss) conditions and directly measuring the temperature change per unit pressure drop, the classic experimental setup used by James Prescott Joule and William Thomson (Lord Kelvin) in the 1850s.

Temperature is entered in Kelvin, heat capacity in J/(mol·K), and the Joule-Thomson coefficient is reported in Kelvin per bar (K/bar), a practical unit for estimating temperature drop across a pressure reduction.